If $x-y=15$ and $xy=4$, what is the value of $x^2+y^2$?
Answer: Squaring both sides of the first equation, we get that $x^2-2xy+y^2=225$. So, we know that $x^2+y^2=225+2xy$. Since $xy=4$, we find $x^2+y^2=225+2(4)=\boxed{233}$.